Conformal Ricci collineations of static spherically symmetric spacetimes

TL;DR

This paper investigates conformal Ricci collineations in static spherically symmetric spacetimes, revealing the maximum number of such symmetries and conditions for infinite symmetries, with examples involving perfect fluid sources.

Contribution

It derives the general form of conformal Ricci collineations for these spacetimes and characterizes the symmetry count in degenerate and non-degenerate Ricci tensor cases.

Findings

Maximum of fifteen conformal Ricci collineations in non-degenerate case

Infinite conformal Ricci collineations in degenerate case

Examples with perfect fluid sources exhibiting these symmetries

Abstract

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter.